Pragmatic factors in conditional reasoning

PRAGMATIC FACTORS IN CONDITIONAL REASONING* María Dolores Valiña, Gloria Seoane, María José Ferraces, & Montserrat Martín University of Santiago de Compostela (Spain) INTRODUCTION One of the questions that has generated most interest in the last decade is the role that pragmatic knowledge has in the reasoning process (see Valiña, 1996, for a revision of the theoretical approaches towards pragmatic reasoning). ____________ * This paper was presented at the NINTH CONFERENCE OF THE EUROPEAN SOCIETY FOR COGNITIVE PSYCHOLOGY - ESCOP, celebrated at the University of Würzburg, Würzburg, Germany (September, 4-8, 1996). A posterior version of this work was published in J. Hoffmann & A. Sebald (Eds). Proceedings of the Ninth Conference of the European Society for Cognitive Psychology (p.142). Pabst Science Publishers. Lengerich. The objective of this experiment is, precisely, to determine in what way the subjects' knowledge of the real world modulates their performance in a conditional reasoning task. In a previous experiment, carried out by the authors, the subjects were presented with the three versions of Wason's selection task (Wason, 1966, 1968), with three types of content (abstract, thematic-permission and thematic-obligation). The results of this experiment showed the importance of factors related to knowledge in executing a metainference task, such as the task of selecting four cards. Indeed, this effect cannot be understood as a mere facilitation of concrete content, faced with the abstract content of the rule. In fact, a better performance was registered in the versions which included a deontic relation, both in abstract and thematic content. Besides, the worst results were obtained with the rule, with a thematic content, which expressed a relation of possibility. This improvement in reasoning could be explained by the proposals of the Theory of Pragmatic Reasoning Schemas (Cheng and Holyoak, 1985, 1989; Cheng, Holyoak, Nisbett & Oliver, 1986; Holyoak and Cheng, 1995). From this perspective, in the two tasks which register a higher number of correct answers, the subjects would be using a schema similar to that of "Obligation". However, it is difficult to explain other results by way of this theoretical proposal, such as the differences in performance registered between the two thematic versions, with both being similar to a pragmatic schema, either of obligation ("thematic2") or of permission ("thematic-1"). However, using the Theory of Mental Models (Johnson-Laird 1983; Johnson-Laird and Byrne, 1991), it is possible to predict and explain the differences in performance between conditionals which express a deontic relation, of “necessity” and conditionals which present a mere “possibility”. In this respect, as Johnson-Laird and Byrne indicated (1992; Byrne and Johnson-Laird, 1992), the “deontic framework” or “epistemic” of the conditional relation may be modulating the subjects' reasoning. Also, the results of Valiña and colleagues (1996) only allow us to verify the influence of the character of “necessity” of a conditional relation, when the subjects are reasoning about a metainference task, such as the selection task. However, is this an influence that may be generalised to other conditional inference tasks?. We designed this experiment to answer this question. Our interest in this experiment is not, therefore, to analyse the influence of the content (abstract vs. thematic) on the subjects' conditional reasoning, as this has been dealt with previously by the authors (Seoane and Valiña, 1988). In fact, we only used conditional arguments, with thematic content, as experimental material. In our opinion, questions relating to the possible effect of thematic facilitation have generated abundant experimental investigation in the last twenty years, but is now a theme that is practically exhausted, given that, as we previously indicated, the influence of knowledge on pragmatic reasoning is more complex than that of a mere facilitation of thematic versus abstract content. In this experiment we tried to determine, precisely, the importance of the variable which we refer to as “the probability of empirical frequency” on conditional reasoning (see Valiña and colleagues, 1992a, b). This refers to the frequency with which the expressed relation between antecedent and consequent in conditional statements, occurs in the real world. This offers three levels, which refer to the grade of empirical occurrence: “deterministic”, “probabilistic” and “without relation”. In this respect, we consider the deterministic relation similar to a relation of “empirical necessity” (the relation expressed in the conditional statement always happens), while the “probabilistic” relation presents a character of “empirical possibility” (which only happens sometimes in the real world). If, as is proposed from the theory of mental models, subjects reason by elaborating analogical representations of the real world, it would be expected that reasoning with conditional statements in which “empirical possibilities” are expressed will be different from the reasoning involved with statements which imply “empirical necessities”. More precisely, and in agreement with Johnson-Laird's proposals (Johnson-Laird and Byrne, 1992; Byrne and Johnson-Laird, 1992), reasoning about a “necessary” argument requires the elaboration of a unique, explicit mental model of the situation. However, if the situation is of a “probable” conditional statement, that may or may not occur in the real world, then it would be necessary to elaborate an explicit mental model and an implicit model. It may therefore be expected that the subjects will manifest more correct reasoning with conditional statements, that they express a necessary (deterministic) relation, than if the relation is possible (probabilistic). In the latter case the number of mental models necessary to produce the conclusion will be greater, which will lead to an increase in the load on operative memory, and will definitively mean an increase in the number of errors. We have also manipulated another two variables: the “type of conditional rule” and the “availability”. The first offers four levels which correspond to the four types of conditional inference rules proposed by propositional logic. The manipulation of the “type of rule” variable will allow us to check how our results support the predictions of the theory of mental models (JohnsonLaird, 1983; JohnsonLaird & Byrne, 1991), or those of its revised version (Evans, 1993), developed within the framework of Evan's theory of heuristicanalytical processes. Based on the theory of mental models, the following is predictable: 1) the Modus Ponens rule is produced more often than Modus Tollens, 2) Modus Ponens and the rule of Affirmation of the Consequent will occur with the same frequency, 3) the rule of Affirmation of the Consequent will be produced more often than the rule of Denial of Antecedent, and 4) the rules of Modus Ponens and Affirmation of Consequent will be more frequent than those of Modus Tollens and Denial of Antecedent. Evans (1993) indicated that the predictions offered by Johnson-Laird (1983; JohnsonLaird & Byrne, 1991) do not always fit the data. He developed a “revised version” of the theory of mental models, with the intention of being able to explain some of the empirical results registered in experimental investigation about conditional inference, that are not justified by the original version of the theory of mental models. Some of the empirical predictions proposed by Evans, with regard to the generation of the four modalities of conditional inference, coincide with or differ from those proposed by Johnson-Laird (1983; JohnsonLaird & Byrne, 1991). These are the following: 1) The MP rule is produced more frequently than MT, 2) the MP rule is generated more often, being even more frequent than the AC rule, 3) the AC and DA rules will occur with approximately the same frequency, and 4) the MP and AC rules will occur more often than those of MT and DA. Finally, the third variable manipulated was The degree of availability of the content was manipulated, selecting the professions of the people in it, that were included in the premises. These people could have an available profession for the subjects (for example, "if the workman falls from the tenth floor he will hurt himself), while in the other eight items a nonavailable profession was presented (for example,"if the plasterer falls from the tenth floor, then he will hurt himself). We have used with conditional arguments, people with available professions (eg. singer, clown, philosopher, biologist, workman etc.), and nonavailable (eg. soprano, axiologist, tightrope walker, malacologist, plasterer, etc.), selected from a previous standardising study carried out by one of the authors. In previous studies these had been used in a series of experiments based upon the study of syllogistic reasoning, with q uantifiers of natural language, including syllogisms in narrative texts (Valiña 1985, 1988; Valiña & De Vega, 1988). Finally, two problems of each rule of propositional logic were included for both types of content (2 Modus Ponens, 2 Modus Tollens, 2 Affirmation of the Consequent, and 2 Denial of the Antecedent). The problems were randomised and their order of presentation in the booklets was random and inverse random. The experimental paradigm used was an answer selection paradigm. The task the subjects faced was to select the conclusion that was logically deduced from the premises. Also, they had to mark with a cross in a seven point scale, the degree of certainty that they had in the correction of their choice. This scale went from "not at all certain" to "completely certain", with an intermediate step for "undecided". The experiment was carried out in a single experimental session, in the class where the students normally have lessons. Half of the subjects, randomly selected, received the booklet with the items presented in random order, and the other half received another booklet with the items in inverse random order. Once the instructions had been read out loud and any problems resolved, the subjects carried out the task without a time limit. RESULTS The data from 6 subjects was eliminated for carrying out the analysis as they had not completed the task. A) Type of Answer The paradigm used in this experiment was, as previously noted, an answer selection paradigm. The task was to select the conclusion or conclusions that they considered possible to logically deduce from the premises. Three conclusions were presented for each item. The “type 1" answer corresponded to the affirmative conclusion, “type 2" to the negative conclusion and "type 3" to the non-propositional, meaning it was not possible to deduce any conclusion. In relation to the percentage of subjects who selected each of the three possible alternatives for each type of rule, in each experimental condition, the most frequently selected answer in the Modus Ponens rule was the affirmative conclusion, which is logically correct. This percentage is reduced in line with the probability of empirical occurrence between antecedent and consequent of the conditional statement. More precisely, the highest percentages of selection of the correct answer was registered in the “deterministic” condition, while a lower frequency of selection of the correct answer appeared in the “without relation” condition. In this case, the subjects were not able to establish any particular link between the events mentioned in the rule and the real world. A higher frequency of rejection of the problem was registered in this task, which is reflected in an increase in the selection of the nonpropositional alternative. In the case of the Modus Tollens rule, the most selected answer was the conclusion which in this case is correct. However, the percentage of subjects who reached the logically correct answer is less than in the Modus Ponens rule. Despite this, the decreasing progression remains the same, throughout the three conditions of empirical occurrence: deterministicprobabilistic-without relation. Therefore, in Modus Tollens the deterministic condition is also that which registered a greater percentage of subjects who selected the correct answer, followed by the probabilistic condition. Nonetheless, the percentage of subjects who selected the non-propositional alternative increased with the problems of the “without relation” condition. This increase is greater than that registered in the same condition with the Modus Ponens rule. Accordingly, the correct answer is that which is selected most with the Modus Ponens and Modus Tollens rules, in agreement with the criteria of formal logic (an affirmative conclusion for MP and a negative conclusion for MT). In the rules of Affirmation of the Consequent and Denial of the Antecedent, the condition where the greatest percentage of correct selections occurs ("type 3" answer) was in “without relation”. However, when the empirical occurrence was deterministic or probabilistic, there was an increase in the tendency to make biconditional interpretations of the statement, which was reflected in an increase of the selection of “type 1” and “type 2” answers, respectively. Therefore, when the subjects reasoned about AC or DA rules, where there was no empirical relation between the antecedent and the consequent, they mainly selected the answer that showed that no conclusion could be deduced from the premises, being the correct alternative, according to logic. However, when the statement expressed a deterministic or probabilistic empirical relation, there were differences between both rules (AC and DA) with regard to the type of answer most frequently selected. When the subjects had to reason about AC problems, they most frequently selected the “type l” answer, while with DA problems they mainly tended to select “type 2”. This may indicate that the increase in the empirical frequency of the content of the rules is accompanied by an increase in the subjects' tendency to carry out biconditional interpretations of the premises, while in the case of conditions “without relation”, this tendency is "blocked", and as a consequence the subjects considered that it was not possible to deduce any conclusion. Indeed, it is precisely the choice of this answer in the “without relation” condition which raises the percentage of correct answers with AC and DA rules. In relation to the percentage of subjects who selected the “type 3” answer ("no conclusion deduced") was greater in the non-logical rules than in the logical rules. In turn, this alternative was that which was most selected when the subjects reasoned about statements where there was no relation between their elements. B) Number of Correct Answers The number of correct answers which each subject had in his booklet was added up, following the criteria of formal logic. An ANOVA 3 x 2 x 4 was made (probability of occurrence x availability x type of rule), using the number of correct answers as a dependent variable. In this analysis a significant effect was registered of the type of rule variable (F(l.64, 77.26)=14.14; p< .0001;  =.54797), with relation to the number of correct answers. The highest number of correct answers were registered when the subjects reasoned about Modus Ponens problems (MP=82.82%), followed by those obtained with Modus Tollens problems (M MT =62.85%) and Denial of the Antecedent (M DA =50.86%). Finally, the lowest percentages of logical successes were obtained with Affirmation of the Consequent problems (MAC=43.23%). The corresponding contrasts carried out afterwards indicated that there were significant differences in the selection of correct answers between Modus Ponens and Modus Tollens (t=19.14; p<.0001), as well as between these two rules with regard to the Affinnation of the Consequent rule (t= 18.465; p<.001). However, no significant differences were registered between the number of correct answers with the Affirmation of the Consequent and Denial of the Antecedent rules. Similarly, a significant interactive effect was registered between probability of empirical occurrence x type of rule (F(3.58, 168.42); p< .0001; = .59724). As may be seen in Figure 1, with the Modus Ponens rule, when a deterministic relation was presented, the highest number of correct answers was obtained. Specifically, the following decreasing progression was registered in the number of logically correct answers, between experimental conditions: deterministic (96.35%), probabilistic (81.25%) and without relation (70.85%). The same progression is maintained with the Modus Tollens rule, even if the number of correct answers in the three levels of empirical occurrence is lower than in the MP rule (70.33% - 62.5% - 55.73%, respectively). However, in the rules of Affirmation of the Consequent and Denial of the Antecedent, this progression was different. More specifically, in the Affirmation of the Consequent rule, the decreasing progression with regard to the number of correct answers was the following: without relation (54.18%), deterministic (38.53%) and probabilistic (36.98%). The Denial of the Antecedent showed themselves to be more certain about their answers (M DET =6.27) than when they reasoned about statements that only occur with certain frequency, or that were probabilistic (M PROB =6.18). Finally, arguments where there is no empirical relation between antecedent and consequent are those which provoked less certainty in the subjects' reasoning (M WR =6.06). Subsequent contrasts showed differences in the deterministic condition compared to the other two (t = 6.533; p< .014). DISCUSSION Significant differences were registered in the number of correct answers, with regard to the type of rule. Correct performance resulted from the following decreasing progression, by way of the four rules: Modus Ponens-Modus Tollens-Denial of the Antecedent-Affirmation of the Consequent. The best performance was obtained, therefore, when the subjects reasoned about Modus Ponens rules, followed by Modus Tollens rules, as is predicted by the original and revised version of the Theory of Mental Models. For Johnson-Laird (1983; Johnson-Laird and Byrne, 1991), these results are due to the fact that, in the case of Modus Ponens, the subjects generate the correct answer directly from the explicit model that they originally elaborate in order to reason. When the subjects reason about MP problems they only elaborate an explicit and implicit model, that represents possible alternative models that are not developed at first. From the minor premise of a MP argument, the subjects do not need to develop this implicit model. Therefore, they will focus their attention on the initial explicit model, and from there will generate the conclusion immediately. In turn, Modus Tollens is less frequent than Modus Ponens, as the conclusion cannot be directly generated from the explicit model, but instead by developing the possible implicit models. Regarding the minor premise of MT, reasoning with this rule requires the elimination of the explicit model, as the subjects cannot reason about a premise that is not included in this model. Consequently, they will have to develop alternative implicit models. If they make a conditional interpretation of the statement, then MT will be generated through the elaboration of three models, whereas if the subjects interpret the relation as biconditional, then two models will be developed. In any case, the number of mental models necessary in MT is greater than in the MP rule. This implies that the load on operative memory will be greater, and accordingly, performance will be worse. Evans (1993) coincides with Johnson-Laird's theory in predicting a higher frequency of problems with Modus Ponens than with Modus Tollens, but he considers that in the original version there is no clear explanation of how the models are elaborated, when they have to reason about Modus Tollens problems. In the revised version of the Theory of Mental Models, the author proposes that the subjects start elaborating an initial representation, that includes the exhaustive representation of the affirmative values, but implicit representation of the negative values. According to the author, "subjects may draw inferences if either the premise is exhaustively represented in the current model, or if all models in wich it occurs are explicity represented" ("P1" principle, Evans, 1993, p. 7). MP inference adjusts to the previous principle, but not that of MT. In this sense, MP may be generated immediately from the initial representation, as "p" is exhaustively represented, but MT is not, as the premise "not q" is not totally represented. The revised version of the theory also proposes that when a subject has to reason about a premise that is not included in the explicit model, he or she will try to develop an implicit model. However, this may be successful or not, and so may generate the correct inference or fail. Similarly, as well as the number of correct logical answers, we have used as a dependent variable certainty of answer. The greater complexity of reasoning with MT and importantly, the greater load on operative memory, explain the lesser certainty registered in MT with regard to MP. In the same way, the non-propositional alternative was selected with greater frequency in the MT rule than in the MP. This result could be explained within the framework of the Theory of Mental Models, bearing in mind that in reasoning about a MT the explicit model is eliminated, and subjects only have the implicit model on hand, that they will have to develop to be able to generate the correct inference. However, on occasions this model is not developed, with the direct conclusion that “it is not possible to deduce any conclusion”. In the MP, the percentage of subjects who selected the non-propositional alternative is less, as in this case the subjects are reasoning directly from the initial explicit model. Our results also show that the MP and MT rules were more frequently developed than those of AC and DA. These results do not support either of the two versions of the theory, according to which the MP and AC rules occur more often than those of MT and DA. On one hand, the original version of the theory predicts the higher occurrence of MP and AC with regard to the explicit representation in the initial model of the affirmative values, and not of the negative. For Evans, the higher frequency of MP and AC was due to the fact that: “inferences will be more often made if the conditions for inference are met in the initial implicit representation and less often if fleshing out is required” (P2 principle, formulated by Evans, 1993, p. 7). Unlike the original version of the theory, which predicts a similar frequency in the production of MP and AC, and supporting the prediction of the revised version, we registered a higher frequency in the production of MP with regard to AC. While JohnsonLaird and Byrne (1991) justify their prediction by pointing out that a conditional may be initially represented by a model where “p” is not exhaustively represented, for Evans an inference is only produced if the premise is exhaustively represented in a model, or if all the models have been developed (the P1 principle, proposed by the author) . For this reason, only MP is directly produced, and AC needs to be produced in a biconditional interpretation of the statement. The results obtained with the “type of rule” variable partially support the Theory of Mental Models, and, more so, the revised version of the theory. To sum up: a) MP takes place more often than MT, as is proposed by both versions, b) MP is more frequent than the AC rule, and, in turn, the AC rule is produced with a similar frequency to the DA rule; both results support the predictions of the revised version of the theory, and do not confirm the predictions of the original version, and c) the MP and AC rules are produced more often than the MT and DA rules. This prediction, from the two versions of the theory, is not confirmed by our results. The results of this investigation confirm our empirical expectations regarding the importance of knowledge about reasoning, in line with results from previous investigations (Valiña and colleagues, 1992a, b). We registered a significant interactive effect on the number of correct answers between the type of rule and probability of empirical occurrence of the statements. Thus, just as Johnson-Laird and Byrne (1992); Byrne and Johnson-Laird (1992) proposed, the difficulty in the production of the four rules of inference is modulated by the necessary or probable character of the relation which they express. According to the authors, when subjects reason about a deontic or necessary relation (which we have called deterministic), they only need to elaborate an explicit model of the situation to produce the correct in ference. However, when they reason about a probabilistic relation, they have to contemplate at least two alternative possibilities, given that the relation may or may not occur. Therefore, they will have to elaborate an explicit model, from the information mentioned in the rule, and an implicit model. The results of our experiment support this previous proposal. Effectively, the best performance with Modus Ponens and Modus Tollens rules was registered with statements which expressed a deterministic relation. However, as previously shown, with MT problems performance was worse, as the structure of the rule means that the subjects are not able to reason directly from a single initial explicit model. Furthermore, in the Modus Tollens rule, worse reasoning was observed with probabilistic relations. In this case, added to the inherent difficulties in the formal structure of MT, was the fact that the probabilistic relation means that the subject had to contemplate various alternative models in order to produce the conclusion. Similarly, Byrne and Johnson-Laird (1992, experiment 3), observed that the presence of a probabilistic modal verb in statements converted the relation into a fact that may or may not occur. As a consequence, in order to reason, the subjects had to elaborate an explicit model (that reveals the event occurrence mentioned in the rule) and an implicit model (that represents the potential possibility that an event may not occur). However, the presence of a deontic modal verb indicated to the subjects that there was no possible alternative to the event mentioned in the statement. In this respect, the determinism in the relation guided the subjects towards the construction of a single explicit model that expressed the occurrence of certainty in their answers increased. Nonetheless, one of the predictions made regarding availability of the scenario was not confirmed. In line with Pollard and Evans (1987), where the influence of contextcontent variables on reasoning was proposed, we expected to register a significant interactive effect between the empirical frequency of the statements and availability of the scenario where they were included. We hoped to obtain a higher number of correct answers and greater certainty of answers when the subjects reasoned about deterministic relations, presented in accessible contexts. Similarly, the worst degree of performance and lowest certainty of answer would be registered when the subjects reasoned about statements “without relation”, in non-avaible contexts. However, these predictions were not confirmed, as we did not register the expected interactive effect. In spite of this, in the context of this experiment, when we refer to “available scenarios”, we are simply referring to conditional arguments which include available professions. Perhaps the way of manipulating this variable and the type of task presented may explain the absence of significant effects of this factor on correct performance. 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